Volume of Polyhedra


Astronomy research
Software instruments
   Stellar equation of states
   EOS with ionization
   EOS for supernovae
   Chemical potentials
   Stellar atmospheres

   Voigt Function
   Jeans escape
   Polytropic stars
   Cold white dwarfs
   Adiabatic white dwarfs

   Cold neutron stars
   Stellar opacities
   Neutrino energy loss rates
   Ephemeris routines
   Fermi-Dirac functions

   Polyhedra volume
   Plane - cube intersection
   Coating an ellipsoid

   Nuclear reaction networks
   Nuclear statistical equilibrium
   Laminar deflagrations
   CJ detonations
   ZND detonations

   Fitting to conic sections
   Unusual linear algebra
   Derivatives on uneven grids
   Pentadiagonal solver
   Quadratics, Cubics, Quartics

   Supernova light curves
   Exact Riemann solutions
   1D PPM hydrodynamics
   Hydrodynamic test cases
   Galactic chemical evolution

   Universal two-body problem
   Circular and elliptical 3 body
   The pendulum


   Zingale's software
   Brown's dStar
   GR1D code
   Iliadis' STARLIB database
   Herwig's NuGRID
   Meyer's NetNuc
cococubed and AAS Videos
Bicycle adventures

AAS Journals
2019 Digital Infrastructure
2019 JINA R-process Workshop
2019 MESA Marketplace
2019 MESA Summer School
2019 AST111 Earned Admission
Teaching materials
Education and Public Outreach

Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.

A pre-requisite to figuring out the volume of a cube cut by a plane is to calculate the volume of a polyhedron, be it convex or non-convex.

The tool and data in polyhedra_volume.tbz compute the volume for 10 tetrahedra, 5 cubes, 5 regular octahedra, 5 rhombic dodecaheda, 1 regular dodecahedron, 1 regular icosahedron, 1 rhombic triacontahedron, 1 disdyakis triacontahedron (left image below), 1 snub cube, and 1 small stellated dodecahedron (non-convex, right image below). Guidance is given in the tool on how to create data files for other polyhedra. The calculated volumes of these polyhedra are then compared to the volumes given by Mathematica, with the differences shown to be near floating point zero.

* *

Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer co-authorship as appropriate.